The Goldbach Mirror II: Geometric Foundations of Conductor Rigidity and the Static Conduit in GSp(4)

Building on the algebraic framework established in the companion paper (Zenodo: 10.5281/zenodo.18684892), we introduce Chen's ratio ρ(N,p) = log 𝒩(JN,p) / log N as a normalised measure of the conductor of the Goldbach–Frey Jacobian in the Siegel moduli space. Computational scanning over N ∈ [10², 10⁴] reveals that Goldbach pairs are rigidly confined to a narrow ρ-band—the static conduit stability band—while composite decompositions spread over a range roughly three times wider. At N = 2^k, the odd radical of the static conduit vanishes, producing dramatic conductor dips that isolate the pure boundary-prime structure. We formalise these observations through a geometric obstruction analysis and identify the precise analytic gap (effective GSp(4) Sato–Tate equidistribution) required to convert this framework into a proof of the Goldbach conjecture.